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Extreme value theory with operator norming

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Abstract

A new approach to extreme value theory is presented for vector data with heavy tails. The tail index is allowed to vary with direction, where the directions are not necessarily along the coordinate axes. Basic asymptotic theory is developed, using operator regular variation and extremal integrals. A test is proposed to judge whether the tail index varies with direction in any given data set.

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Authors and Affiliations

  1. Department of Statistics & Probability, Michigan State University, East Lansing, MI, 48824, USA

    Mark M. Meerschaert

  2. Fachbereich Mathematik, Universität Siegen, 57068, Siegen, Germany

    Hans-Peter Scheffler

  3. Department of Statistics, University of Michigan, Ann Arbor, MI, 48109, USA

    Stilian A. Stoev

Authors
  1. Mark M. Meerschaert
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  2. Hans-Peter Scheffler
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  3. Stilian A. Stoev
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Corresponding author

Correspondence to Stilian A. Stoev.

Additional information

Mark M. Meerschaert was partially supported by NSF grant DMS-1025486 and NIH grant R01-EB012079.

Stilian A. Stoev was partially supported by the NSF grant DMS–1106695 at the University of Michigan.

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Meerschaert, M.M., Scheffler, HP. & Stoev, S.A. Extreme value theory with operator norming. Extremes 16, 407–428 (2013). https://doi.org/10.1007/s10687-012-0166-x

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  • DOI: https://doi.org/10.1007/s10687-012-0166-x

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